Are the hops in beer wort still dangerous to dogs after being composted?

I make beer. I make compost. I would like to use the former, to assist the latter. However, as most home-brewers already know, hops are very dangerous to dogs. This made me wonder: If I use the wort that I strain out of my homemade beer, will the hops in the gooey mess still be dangerous to my dogs if they get into the compost days/weeks/months later?

Did you make this instructable?

. According to the Wikipedia article on dog health (my emphasis): "Even small amounts of hops can trigger a potentially deadly reaction, even if the hops are "spent" after use in brewing." . A Q&D search did not turn up just what about hops is toxic, so I can't tell if it would decompose during composting or not. :( Better safe than sorry.